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20.88 (2022)

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Let $u$ be an element of a free group $F_r$. Is it true that there is $v \in F_r$ (that depends on $u$) that cannot be a subword of any cyclically reduced word $\phi(u)$, where $\phi$ is an automorphism of $F_r$?

Contributor: V. Shpilrain

Progress

*Yes, it is true (L. Koch-Hyde, S. O’Connor, E. Olive, V. Shpilrain, Preprint, 2025, https://arxiv.org/abs/2505.00477).

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